The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  X  1  2  1  1  1  1  0  1  1 X+2  1  1 X+2  1  1  2  2  1  1  0 X+2  0  1  1  1  1  1  1 X+2 X+2  1  1  1  1  0  1  1  X X+2  1  1  1  X  X  1  1  2 X+2  1  1  1  1 X+2  X  1  1  1 X+2  2  0  2  1  2  X  1  1  1  1  1  0  1  X  0  X  1  0  1  1  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  1  3  1  0 X+3  2 X+3  1 X+2  1  1 X+2  1  1  0  0  1  1 X+1 X+1  1  1  1  3  2  3 X+3 X+1  2  1  1  X  X  2  1  1 X+2  1  1  1 X+3  X  X  1  1 X+1  X  1  1  X X+3  3  3  1  1 X+3  2  1  1  1  1  1  0  1  0  1 X+3 X+3 X+1 X+2  1 X+2  1  2  X  X  X X+2  2 X+1
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  X  2  X  2  X  X  2  2  X X+2  2  2  0 X+2  0  0  X  X  0  0  0  0  2  2  X  0  X  X  X  2  2 X+2  X  X X+2  X  0  X  X  X X+2  0  0 X+2  2 X+2  X  X  2  2 X+2  2  2  0  2  2  X  2 X+2  2  0  0 X+2 X+2 X+2  X  0  0  X  X  2  X  X  X X+2  0  X  0  X  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  2  0  0  2  2  0  2  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  2  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  0  0  0  2  2  2  2  2  2  0  2  2  2
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  0  0  2  2  2  2  2  0  2  0  0  2  2  0  0  2  0  2  0  2  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  2  2  2  0  2  0  2  2  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  0  0  0  0  0  2  2  0  2  0  0  0  0  2  2  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  2  2  2  2  0  2  2  2  2  2  0  0  2  0  2  0  0  2  2  2  2  0  2  0  0  2  0  2  0  0  0  0  2  2  0  2  0  0  2  2  0  0  0  2  2  0  0  0  2  0  2  2  2  2  2  0  2  0  0  2  0  0  2  0  0  0  0  2  0  0  2  2  2  0  2  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  2  2  2  2  2  2  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  0  2  0  0  2  0  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  0  0  0  2  2  0  0  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  2  0  0  0  2  2  2  2  0  2  0  2  2  0  0  2  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  0  2  0  0  0  2  0  2  2  2  0  2  2  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  2  2  2  2  2  2  2  0  0  0  0  2  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  2  0  2  0  0  0  2  2  0  2  2  2  2  0  2

generates a code of length 90 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+40x^78+68x^79+178x^80+224x^81+408x^82+528x^83+691x^84+892x^85+963x^86+1018x^87+1143x^88+1370x^89+1302x^90+1382x^91+1320x^92+1102x^93+1003x^94+852x^95+560x^96+410x^97+292x^98+216x^99+162x^100+84x^101+58x^102+30x^103+25x^104+10x^105+18x^106+2x^107+9x^108+2x^109+7x^110+5x^112+2x^113+4x^114+1x^116+1x^118+1x^124

The gray image is a code over GF(2) with n=360, k=14 and d=156.
This code was found by Heurico 1.16 in 23.3 seconds.